a) Solve the initial value problem y" + 2y' + 5y = 0, y(0) = 4 and y'(0) = -1. b) Describe the behavior of the solution as t goes to infinity. Assume the input of y is t, i.e. y(t).

Q: What are the P(x) and Q(x) of y' =y-xy³e2Xrespectively?

A: Given the differential equation is: Since

Q: Solve y" – 2y' – 3y = 3t² – 5 using the Method of Undetermined Coefficients.

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Q: 4x y" - 5y + 4y = ¹, y(0) = 0, y'(0) = 10/3 e

A: Please find attachment

Q: Verify whether yı = 3t4 and y2 = 4 t-2 form a fundamental set of solutions for f y" +7t y' + 8 y =…

A: We will verify the given statement.

Q: a) 2xy dx+(1+x²)dy=0 b) y'+(4/x)y=x* ------by exact method ---by linear method

A:

Q: Show that the function f(t) = 1² – } is a solution of the dif- ferential equation (y')² – 4y = 2.

A: Given:       f(t)=t2−12.Differential equation is: (y')2−4y=2

Q: Solve y + y = 2y = 0, where y (0) - = 3 and y (0 y(t) =

A: y''+y'-2y=0 Auxiliary eqaution m2+m-2=0

Q: let h(y)=(y-3y2)5(y2+2)6  h'(y) in simplified form.

A:

Q: 3. Solve using any technique y" – 2y/ – 3y = 3e",; 7 ", y(0) = 3, y'(0)

A: We have to solve given problem:

Q: 3. Solve y" – 2y' + 5y = 0, y(0) = 5, y'(0) = –3. %3D

A:

Q: Show that y = 5x2 + 2 is a solution to the DE xy' +(2)/(5) y" = 2y.

A: To show: y=5 x2+2 is a solution of differential equation xy'+25y''=2y

Q: 5. [10 points] Find the general solution y"-6y' +9y = x*e*

A:

Q: Solve the pollowing: () (^) 2+j =j(xtjy) X = ? y=? (1) (2+j)(3-j2) = a+jb () (x-j2y) -(y-j«)-2tj a:?…

A: (a). Given  2+j1-j = j(x+jy)⇒ 2+j1-j×1+j1+j = -y+jx⇒ 2+2j+j-11+1 = -y + jx⇒ 12+32j = -y + jxBy…

Q: y' = (x - 1)(y-2), y(2) = 4

A:

Q: ye x, (21x) satisfie s Show that the equation

A: Given: The given equation is xy''+n+1y'+y=0  ,  y=xn22x

Q: Obtain general solution. 1) y''-y=ex-4

A:

Q: Are the functions y₁(x) = e, y2(x) = ze a fundamental set of solutions for the equation y" - 2y + y…

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Q: Determine (without solving the problem) an interval in which the solution of (9-1²)y + 2ty = 4t²,…

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Q: If these two y's, y1=e^tcos(t) and y2(t)=e^tsin(t) are both solutions to y''+j(t)y'+k(t)y=0, how do…

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Q: 3) Consider the IVP y' = x − 2y, y(0) = 1/2. Determine which of the two curves shown in the figure…

A: The solution of the differential equation is defined as the function that satisfies the equation.…

Q: Q2) Solve: y" - 5y' +6y=H(t-1), y(0) = 0, y'(0) = 1.

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Q: ) Verify that y=e-2x is a solution of equation x(y")3+ (y')4 – y = 0

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Q: Find the general solution of x2y" - (2a-1)xy' + a²y = xa+1 where a is a constant.

A: Given  x2y'' - 2a - 1xy + a2y = xa+1  ----------(1)           This is Cauchy's homogeneous…

Q: Solve y" -8y' +16y = 0

A:

Q: 2a) find a solution of y" (x) = y(x) that passes the origin and go trhout the point (In(2),-).

A:

Q: Find the GS of 2 (x - α)² = where a is an arbitrary constant and you may want to consider "pilot" y₁…

A: As per the question we are given the following nonlinear first order differential equation…

Q: Evaluate the general solution of y""=e4x + sinx

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Q: (1) y "'+ y "– 2y = 3+2cosx

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Q: y" + 7y' + 10y = -1lte".

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Q: 5) Form a DE by eliminating the arbitrary constants from the equation y = asin(4x + 1).

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Q: Find solution of IVP y" - 4y - 5y = 0 y(1) = 8, y'(1) = -5.

A: Given the differential equation is                        y''-4y'-5y=0, y(1)=8, y'(1)=-5.

Q: Question Evaluate the double integral ff f(x,y)dA where f(x, y) = (0, 3), and (3,0). D -1 y² + 1 and…

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Q: Eliminate the constant: 3x =c₁e²x + c₁₂e ³x Oy"-y'-6y=0 Oy"-5y'+6y=0 Oy"+y'-6y=0 Oy"+ 5y'+6y=0

A: Application of differential equations